If | , * 20 c a_1 & b_1 & c_1 a_2 & b_2 & c_2 a_3 & b_3 & c_3 , |… - Vidyadip

MCQ

If $\left| {\,\begin{array}{*{20}{c}}{{a_1}}&{{b_1}}&{{c_1}}\\{{a_2}}&{{b_2}}&{{c_2}}\\{{a_3}}&{{b_3}}&{{c_3}}\end{array}\,} \right| = 5$; then the value of $\left| {\,\begin{array}{*{20}{c}}{{b_2}{c_3} - {b_3}{c_2}}&{{c_2}{a_3} - {c_3}{a_2}}&{{a_2}{b_3} - {a_3}{b_2}}\\{{b_3}{c_1} - {b_1}{c_3}}&{{c_3}{a_1} - {c_1}{a_3}}&{{a_3}{b_1} - {a_1}{b_3}}\\{{b_1}{c_2} - {b_2}{c_1}}&{{c_1}{a_2} - {c_2}{a_1}}&{{a_1}{b_2} - {a_2}{b_1}}\end{array}\,} \right|$is

A
$5$
✓
$25$
C
$125$
D
$0$

✓

Answer

Correct option: B.

$25$

b
(b) Required determinant
$|adj\,A|$=$|A{|^{3 - 1}}$,$\,{\rm{where}}A = \left| {\,\begin{array}{*{20}{c}}{{a_1}}&{{b_1}}&{{c_1}}\\{{a_2}}&{{b_2}}&{{c_2}}\\{{a_3}}&{{b_3}}&{{c_3}}\end{array}\,} \right|$
$ = {5^2} = 25,$ $(\because \,\,|adj\,A| = |a{|^{n - 1}})$

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